Length and time for development of laminar flow in tubes following a step increase of volume flux

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• 作者：Rafeed A. Chaudhury ; Marcus Herrmann ; David H. Frakes…
• 刊名：Experiments in Fluids
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：56
• 期：1
• 全文大小：1,982 KB
• 参考文献：1. Adrian, RJ, Westerweel, J (2010) Particle Image Velocimetry. Cambridge University Press, Cambridge
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• 刊物类别：Engineering
• 刊物主题：Engineering Fluid Dynamics
  Fluids
  Industrial Chemistry and Chemical Engineering
  Measurement Science and Instrumentation
  Thermodynamics
  Theoretical and Applied Mechanics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1114

文摘

Laminar flows starting up from rest in round tubes are relevant to numerous industrial and biomedical applications. The two most common types are flows driven by an abruptly imposed constant pressure gradient or by an abruptly imposed constant volume flux. Analytical solutions are available for transient, fully developed flows, wherein streamwise development over the entrance length is absent (Szymanski in J de Mathématiques Pures et Appliquées 11:67-07, 1932; Andersson and Tiseth in Chem Eng Commun 112(1):121-33, 1992, respectively). They represent the transient responses of flows in tubes that are very long compared with the entrance length, a condition that is seldom satisfied in biomedical tube networks. This study establishes the entrance (development) length and development time of starting laminar flow in a round tube of finite length driven by a piston pump that produces a step change from zero flow to a constant volume flux for Reynolds numbers between 500 and 3,000. The flows are examined experimentally, using stereographic particle image velocimetry and computationally using computational fluid dynamics, and are then compared with the known analytical solutions for fully developed flow conditions in infinitely long tubes. Results show that step function volume flux start-up flows reach steady state and fully developed flow five times more quickly than those driven by a step function pressure gradient, a 500?% change when compared with existing estimates. Based on these results, we present new, simple guidelines for achieving experimental flows that are fully developed in space and time in realistic (finite) tube geometries. To a first approximation, the time to achieve steady spatially developing flow is nearly equal to the time needed to achieve steady, fully developed flow. Conversely, the entrance length needed to achieve fully developed transient flow is approximately equal to the length needed to achieve fully developed steady flow. Beyond this level of description, the numerical results reveal interaction between the effects of space and time development and nonlinear Reynolds number effects.